让小模型像大模型一样高效推理，只需更少资源。

The reasoning capabilities of large reasoning models (LRMs), such as OpenAI's o1 and DeepSeek-R1, have seen substantial advancements through deep thinking. However, these enhancements come with significant resource demands, underscoring the need for training effective small reasoning models. A critical challenge is that small models possess different reasoning capacities and cognitive trajectories compared with their larger counterparts. Hence, directly distilling chain-of-thought (CoT) rationales from large LRMs to smaller ones can sometimes be ineffective and often requires a substantial amount of annotated data. In this paper, we first introduce a novel Critique-Rethink-Verify (CRV) system, designed for training smaller yet powerful LRMs. Our CRV system consists of multiple LLM agents, each specializing in unique tasks: (i) critiquing the CoT rationales according to the cognitive capabilities of smaller models, (ii) rethinking and refining these CoTs based on the critiques, and (iii) verifying the correctness of the refined results. Building on the CRV system, we further propose the Cognitive Preference Optimization (CogPO) algorithm to continuously enhance the reasoning abilities of smaller models by aligning their reasoning processes with their cognitive capacities. Comprehensive evaluations on challenging reasoning benchmarks demonstrate the efficacy of our CRV+CogPO framework, which outperforms other methods by a large margin.